Algebra

Fields and Galois Theory

Authors:

ISBN: 978-0-387-28930-4 (Print) 978-0-387-31608-6 (Online)

Table of contents (19 chapters)

  1. No Access

    Book Chapter

    Pages 1-13

    Constructibility with Ruler and Compass

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    Book Chapter

    Pages 15-20

    Algebraic Extensions

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    Book Chapter

    Pages 21-32

    Simple Extensions

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    Book Chapter

    Pages 33-43

    Fundamentals of Divisibility

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    Book Chapter

    Pages 45-53

    Prime Factorization in Polynomial Rings. Gauss’s Theorem

  6. No Access

    Book Chapter

    Pages 55-64

    Polynomial Splitting Fields

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    Book Chapter

    Pages 65-73

    Separable Extensions

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    Book Chapter

    Pages 75-82

    Galois Extensions

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    Book Chapter

    Pages 83-92

    Finite Fields, Cyclic Groups and Roots of Unity

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    Book Chapter

    Pages 93-101

    Group Actions

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    Book Chapter

    Pages 103-113

    Applications of Galois Theory to Cyclotomic Fields

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    Book Chapter

    Pages 115-131

    Further Steps into Galois Theory

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    Book Chapter

    Pages 133-141

    Norm and Trace

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    Book Chapter

    Pages 143-164

    Binomial Equations

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    Book Chapter

    Pages 165-190

    Solvability of Equations

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    Book Chapter

    Pages 191-202

    Integral Ring Extensions with Applications to Galois Theory

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    Book Chapter

    Pages 203-208

    The Transcendence of π

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    Book Chapter

    Pages 209-216

    Fundamentals of Transcendental Field Extensions

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    Book Chapter

    Pages 217-230

    Hilbert’s Nullstellensatz